Abstract: Some applications of ratios of normal random variables require both the numerator and denominator of the ratio to be positive if the ratio is to have a meaningful interpretation. In these applications, there may also be substantial likelihood that the variables will assume negative values. An example of such an application is when...
Abstract: I am grateful to Bi and Meyners for their comments on my letter and to the editors of FQ&P for allowing this discussion on equivalency testing. I am glad that the replies to my letter have opened up some of the questions concerning equivalency testing methods which were not adequately discussed by Bi...
Abstract: Bi (2007) discusses equivalency testing (which he terms similarity testing) in a recent paper in Food Quality and Preference and he relies on theory underlying the ‘‘two one-sided tests’’ (TOST) referencing Westlake (1981) and Schuirmann (1981). Bi’s paper contains a useful bibliography on the topic. Although Bi references Berger and Hsu (1996), which...
Abstract: There is frequent interest in establishing whether two products or treatments are essentially equivalent or at parity. Two types of parity hypotheses are defined in this article, an unsurpassed hypothesis and an equality hypothesis. Tables for these two types of parity hypotheses are presented for 2-alternative forced choice and preference data. These two...
Abstract: If X is the Gromov–Hausdorff limit of a sequence of Riemannian manifolds Mni with a uniform lower bound on Ricci curvature, Sormani and Wei have shown that the universal cover ˜X of X exists ; [C....
Abstract: Dependence among responses in using the A-Not A or “Yes-No” task are accounted for in new hypothesis testing models. The new models involve adjustments to Pearson’s and McNemar’s chi-square statistics and to the variance of d‘, a measure of signal detectability or sensitivity. This is paper # 61 when requesting reprints. To request a...
Abstract: Exact tables calculated directly from the probability function of a betabinomial distribution are provided for replicated difference and preference tests. The tables can be used for small experiments when the numbers of replications and trials are not more than jive. This is paper # 54 when requesting reprints. To request a paper, please click...
Abstract: Binomial tests are often used in sensory difference and preference testing. Two assumptions underlie this use: (1) responses are independent and (2) choice probabilities do not vary from trial to trial. In many applications, the latter assumption is violated. In this paper we account for variation in inter-trial choice probabilities using the beta...
Abstract: Ennis and Bi (1998) discussed the beta-binomial (BB) model for replicated diflerence and preference tests. Based on the BB model, tables of the minimum number of choice responses to achieve significance at a ?0.05 are provided for replicated 2-AFC, Duo-Trio, 3-AFC and Triangular tests. The theory underlying the tables, how to use the...
Abstract: Research on the power of discrimination methods in difference and preference tests has both theoretical and practical significance. Power is important to evaluate the sensitivities of tests and determine sample size. Ennis and Bi (I 998, 1999) proposed the beta-binomial distribution to model replicated difference and preference tests with inter-trial variation and analyzed...